mm-1008
===
Subject: Re: Please help. Having problem with simple math
logic
>I have 2 number scales.
>Top scale = 42 through -84
>and
>Bottom scale = 17 through 782
>If 17 on the bottom scale represents 42 on the top scale,
and the same
>goes for 782 on the bottom with -84 on the top, how do I
Žgure out
>any number on the top scale by inputting a number on the
bottom scale.
>(i.e. 261 on the bottom scale = ? on the top scale.
You mean e.g., not i.e. (Why do people use words when they
don¹t
know the meaning?)
But there¹s a more substantive issue: You haven¹t told us what
relationship exists between the two scales. Is it supposed to
be a
straight-line relationship, one where e.g. any interval of 100
points on the bottom scale makes the same width interval on
the top
scale?
If you make that assumption, your problem can be solved. You
have
two (x,y) points, namely (17, 42) and (782, -48), and you
need to
Žnd the equation of the line between them. The slope of that
line
is -90/765, so you use the point-slope form:
top = (-90/765)*(bottom-17) + 782
or
top = (-2/17)*bottom + 784
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com
Address munging may or may not reduce the spam you get; it
surely
reduces the number of useful answers you get.
http://www.cs.tut.Ž/~jkorpela/usenet/laws.html
===
Subject: Re: Please help. Having problem with simple math
logic
>>Top scale = 42 through -84
>>Bottom scale = 17 through 782
>If you make that assumption, your problem can be solved. You
have
>two (x,y) points, namely (17, 42) and (782, -48), and you
need to
>Žnd the equation of the line between them. The slope of that
line
>is -90/765, so you use the point-slope form:
> top = (-90/765)*(bottom-17) + 782
Well _That_ was careless of me! The given point is (17,42),
so the
equation should be
top = (-90/765)(*bottom-17) + 42
or
top = (-2/17)*bottom + 44
which also works with the point (782, -48) as it should.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com
Address munging may or may not reduce the spam you get; it
surely
reduces the number of useful answers you get.
http://www.cs.tut.Ž/~jkorpela/usenet/laws.html
===
Subject: Re: ReL Please help. Having problem with simple
logic.
>>Top scale = 42 through -84
>>Bottom scale = 17 through 782
> The formula is T= (-0.1657)B+ 170.8. That a is negative is
due to
>the fact that the two scales are reversed, a higher value on
one
>corresponds to a lower value on the other.
The given point (17,42) does not work in that formula.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com
Address munging may or may not reduce the spam you get; it
surely
reduces the number of useful answers you get.
http://www.cs.tut.Ž/~jkorpela/usenet/laws.html
===
Subject: Re: Solving normal probability
>I need some serious help with probability. I just cannot get
it.
And what have you done to try to get it, other than simply
copy
the problem into your news posting software?
Please tell us what you tried, and _speciŽcally_ where you got
stuck.
If you need a hint, here¹s one: Your second and third
questions both
require you to apply the Empirical Rule.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com
Address munging may or may not reduce the spam you get; it
surely
reduces the number of useful answers you get.
http://www.cs.tut.Ž/~jkorpela/usenet/laws.html
===
Subject: Re: Yes, your Želd is corrupt
> Some of you may have noticed that I¹ve Žnally focused on
the base
> assumption required to Žght the proof that there is an over
one
> hundred year old deŽnition in core mathematics, as posters
are
> Žnally revealed to be arguing for a relation like xy=uf,
where x and
> y are algebraic integer functions.
> It¹s like someone arguing with you about xy=2, being in the
ring of
> integers, where x can be any integer, as I can even set
u=1, f=2, to
> *get* that value.
> So how have they gotten away with arguing such a position
for months?
> You and other mathematicians have let them because
mathematics is just
> a joke to you, and maybe a way to make money.
> Maybe you know that people just *trust* mathematicians, and
you¹re in
> the Želd to be in an area where the truth doesn¹t matter.
> Your Želd is corrupt. Mathematicians don¹t really care about
> anything but themselves. They are sick and lost.
> You are lost if you are with them.
> James Harris
> This is a crock of bull. If you are right, then I think
everyone who has
> taken math needs to go back and relearn the correct
mathematics. You need
to
> grow up; don¹t worry about this fame and money you claim
that you
deserve.
> You have a physics degree; USE IT!
> What would you do if someone attacked the Želd of physics?
It¹d be the
same
> thing you¹re doing with mathematics. Get help......fast!
Oh yeah, try to shift the focus from your *proven* corruption.
It¹s mathematicians who are defying mathematics.
It¹s mathematicians who are now caught in a stupid lie to
hide an over
one hundred year old error.
It¹s mathematicians who are running from the truth.
Your are corrupt and lost souls.
James Harris
===
Subject: Re: Implicit differentiation help
> Hi i also need help with an implicit differentiation
question. The
> question is to Žn the 2nd derivative as a function of x if
sin y+cos
> y=x. I can get to a Žnal answer but it i cant get rid of
the y
> values i have there. Could anyonehelp me get an answer in
terms of
I think this problem can be attacked primarily by going
through the
motions:
(1) sin(y) + cos(y) = x
Differentiate w.r.t. x:
(2) [cos(y) - sin(y)] * y¹ = 1
Multiply (2) by 1/y¹ to get:
(3) cos(y) - sin(y) = 1/y¹
Now square (1) and (3) to get:
(4) sin^2(y) + 2*sin(y)*cos(y) + cos^2(y) = x^2
(5) sin^2(y) - 2*sin(y)*cos(y) + cos^2(y) = (1/y¹)^2
The previous reorganization is a standard trick, so take
note. Now add (4)
and (5) to get:
(6) 2 = x^2 + (1/y¹)^2
Isolate y¹:
(7) y¹ = sqrt[1/(2 - x^2)]
It¹s your job to Žnish. Note that the square root can be
positive or
negative.
There are other ways of arriving at this equation, but this
one is cleaner
that the Žrst one I thought up. You should be able to proceed
from here.
Hope I didn¹t do too much of your homework for you!
.... Bob
===
Subject: Probability Question from a Computer Course
BACKGROUND:
part that modeled this situation (a sample output from that
part is at
the end of this post):
There are n=10 mines in the water.
A sonar can send one ping at a time, (which will reach all n
mines).
The ping will detect an individual mine with a probability
p=0.05.
Once a mine is detected, it stays detected forever (don¹t
need to
Žnd it again, although a later ping may or may not detect it).
How long will it take to discover all 10 mines?
(The assignment had some other big parts to it; I didn¹t
write it to
Žnd the repeated average of this part. I ran a few trials and
came up
with 67, 49, 46, 65, and 67 pings).
QUESTION:
How would one compute the actual expected value of the number
of pings
required? This was not a part of the assignment, but has been
bugging
me since I¹m also in a beginning probability course.
My thinking so far:
1. The expected number of detections in each ping is 1/2 a
mine, but
that doesn¹t seem to lead anywhere.
2. Each ping is a binomial process with n=10, p=0.05. So on
each ping,
I could calculate the probability of exactly r=0 detections,
r=1
detections, etc.
3. Now I have the probabilities of the 11 possible outcomes
(detected
r=0 mines, r=1, ... ,r=10) of the Žrst ping from 2. I could
calculate
the conditional probabilities of the outcomes of the second
ping:
3.a. Given r=0 mines detected on the Žrst ping, repeat 2.
3.b. Given r=1 mines detected on the Žrst ping, calculate the
10
binomial probabilities of r=0..9 detections, with n=9, p=0.05.
3.c. Given r=2..r=10 on the Žrst ping, similar to 3.b.
So, I would do something like 10! (or is it 10^10?)
computations of the
binomial formula, summing expected values along each branch
of a huge
tree. There must be a nicer way. Any suggestions?
*Sample Output of my program*
---------------------------------------
Creating mine #0
Creating mine #1
Creating mine #2
Creating mine #3
Creating mine #4
Creating mine #5
Creating mine #6
Creating mine #7
Creating mine #8
Creating mine #9
Ping #1
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: false
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: CONTACT! Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 1
Ping #2
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: false
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 1
Ping #3
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: false
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: CONTACT! Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 1
Ping #4
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: false
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 1
Ping #5
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: false
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 1
Ping #6
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: false
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 1
Ping #7
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: false
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 1
Ping #8
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: false
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 1
Ping #9
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: CONTACT! Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 2
Ping #10
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 2
Ping #11
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 2
Ping #12
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 2
Ping #13
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: false
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 2
Ping #14
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: CONTACT! Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 3
Ping #15
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 3
Ping #16
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: false
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: CONTACT! Has been detected: true
mySonar pinged mine #8: no contact Has been detected: false
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 3
Ping #17
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: CONTACT! Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: CONTACT! Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 5
Ping #18
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: CONTACT! Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 5
Ping #19
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 5
Ping #20
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: CONTACT! Has been detected: true
mySonar pinged mine #4: no contact Has been detected: false
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 5
Ping #21
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: CONTACT! Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: CONTACT! Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #22
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: CONTACT! Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: CONTACT! Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #23
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #24
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #25
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #26
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #27
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #28
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #29
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #30
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #31
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: CONTACT! Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #32
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #33
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #34
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #35
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #36
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: CONTACT! Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #37
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #38
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #39
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: false
Total number of objects detected by SONAR so far = 6
Ping #40
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: CONTACT! Has been detected: true
Total number of objects detected by SONAR so far = 7
Ping #41
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 7
Ping #42
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 7
Ping #43
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 7
Ping #44
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: false
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 7
Ping #45
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: CONTACT! Has been detected: true
mySonar pinged mine #5: CONTACT! Has been detected: true
mySonar pinged mine #6: CONTACT! Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 8
Ping #46
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: CONTACT! Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 8
Ping #47
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: CONTACT! Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 8
Ping #48
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: CONTACT! Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 8
Ping #49
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 8
Ping #50
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 8
Ping #51
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 8
Ping #52
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 8
Ping #53
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: false
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 8
Ping #54
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: CONTACT! Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: CONTACT! Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #55
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: CONTACT! Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #56
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: CONTACT! Has been detected: true
mySonar pinged mine #2: CONTACT! Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #57
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #58
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: CONTACT! Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #59
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: CONTACT! Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #60
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: CONTACT! Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #61
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: CONTACT! Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #62
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #63
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #64
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #65
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: CONTACT! Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #66
mySonar pinged mine #0: no contact Has been detected: false
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 9
Ping #67
mySonar pinged mine #0: CONTACT! Has been detected: true
mySonar pinged mine #1: no contact Has been detected: true
mySonar pinged mine #2: no contact Has been detected: true
mySonar pinged mine #3: no contact Has been detected: true
mySonar pinged mine #4: no contact Has been detected: true
mySonar pinged mine #5: no contact Has been detected: true
mySonar pinged mine #6: no contact Has been detected: true
mySonar pinged mine #7: no contact Has been detected: true
mySonar pinged mine #8: no contact Has been detected: true
mySonar pinged mine #9: no contact Has been detected: true
Total number of objects detected by SONAR so far = 10
===
Subject: Re: Probability Question from a Computer Course
>BACKGROUND:
>part that modeled this situation (a sample output from that
part is at
>the end of this post):
>There are n=10 mines in the water.
>A sonar can send one ping at a time, (which will reach all n
mines).
>The ping will detect an individual mine with a probability
p=0.05.
>Once a mine is detected, it stays detected forever (don¹t
need to
>Žnd it again, although a later ping may or may not detect
it).
>How long will it take to discover all 10 mines?
>(The assignment had some other big parts to it; I didn¹t
write it to
>Žnd the repeated average of this part. I ran a few trials
and came up
>with 67, 49, 46, 65, and 67 pings).
>QUESTION:
>How would one compute the actual expected value of the
number of pings
>required? This was not a part of the assignment, but has
been bugging
>me since I¹m also in a beginning probability course.
You¹ll want to check all of the calculations, as I haven¹t had
time to do much double-checking.
For later convenience let q = 1 - p. Let p(k,r) be the
probability that exactly r mines remain undetected after the
Žrst k pings. There are C(n,r) ways of choosing r mines. The
probability that a particular mine remains undetected after k
pings is q^k, so the probability that every mine in a
particular
set of r mines remains undetected after k pings is (q^k)^r =
q^(rk). The probability that a given mine is detected in at
most
k pings is 1 - q^k, so the probability that every mine in a
particular set of n - r mines is detected within k pings is
(1 - q^k)^(n-r). Thus,
p(k,r) = C(n,r)*q^(kr)*(1 - q^k)^(n-r).
In particular, p(k,0) = (1 - q^k)^n (which reassuringly does
approach 1 as k increases!). This isn¹t the probability that
it
will take k pings to detect all n mines, however, but rather
the
probability that it will take at most k pings. The
probability,
P(k), that it will take exactly k pings must be
P(k) = p(k,0) - p(k-1,0) = (1 - q^k)^n - (1 - q^(k-1))^n,
and e, the expected number of steps, must be
e = sum{k > 0; k[(1 - q^k)^n - (1 - q^(k-1))^n]}.
Consider the m-th partial sum e(m):
e(m) =
sum{k=1 to m; k[(1 - q^k)^n - (1 - q^(k-1))^n]} =
sum{k=1 to m; k(1 - q^k)^n} -
sum{k=1 to m; k(1 - q^(k-1))^n} =
sum{k=1 to m; k(1 - q^k)^n} -
sum{k=2 to m; k(1 - q^(k-1))^n} =
sum{k=1 to m; k(1 - q^k)^n} -
sum{k=1 to m-1; (k + 1)(1 - q^k)^n} =
sum{k=1 to m; k(1 - q^k)^n} -
sum{k=1 to m-1; k(1 - q^k)^n} -
sum{k=1 to m-1; (1 - q^k)^n} =
m(1 - q^m)^n - sum{k=1 to m-1; (1 - q^k)^n}.
Now
sum{k=1 to m-1; (1 - q^k)^n} =
sum{k=1 to m-1; sum{j; C(n,j) * (-1)^j * q^(jk)}} =
sum{j=0 to n; (-1)^j * C(n,j)*sum{k=1 to m-1; q^(jk)}} =
(m - 1) +
sum{j=1 to n; (-1)^j * C(n,j)*sum{k=1 to m-1; q^(jk)}} =
(m - 1) +
sum{j=0 to n; (-1)^j * C(n,j) * (q^j - q^jm)/(1 - q^j)}.
Similarly,
m(1 - q^m)^n =
m + sum{j=1 to n; m * C(n,j) * (-1)^j * q^(jm)},
so
e(m) =
1 + sum{j=1 to n; C(n,j)*(-1)^j*
[q^(jm)} - (q^j - q^(jm))/(1 - q^j]}.
Taking the limit as m increases without bound, we get
e = 1 - sum{j=1 to n; C(n,j) * (-1)^j * q^j / (1 - q^j)}. [*]
As a rough check, note that when n = 1 this reduces to
e = 1 + q/(1 - q) = 1/(1 - q) = 1/p,
as expected.
I don¹t immediately see a nice closed form for e in [*], but
this
at least reduces the problem considerably.
Brian
===
Subject: Re: addition
> I need help with adding two numbers (like 1, 2, and maybe
even
> others). How¹s it possible to do it without a calculator?!
Also, what
> does it mean when the book says 1 + 1 + 1? I¹ve only heard
about
> adding two numbers, not three. My calculus teacher wasn¹t
very clear
> about it.
It is considered an abomination to add a number other than 1
to another
number. So if you are confronted with say 50 + 20 you must
break one of
these
larger numbers down to a series of 1s to get back to basic
deŽnitions.
(Hint,
choose the smaller one.) So we get 50 + (1 + 1 + 1 ..... +1)
You move the
Žrst 1 outside the parentheses and you get 51 + (1+1+ ....
+1) You keep
going
like this one at a time and Žnally you will end up with 69 +
1 = 70. The
general result is known as the ones theorem. You must always
apply the ones
theroem whenever you have numbers to add together.
The reason your calculus teacher would not talk about adding
three numbers
is
that is also considered an abomination. This all goes back to
Noah¹s Ark
where
the animals were in twos - never threes. However, you can
achieve the same
result by applying the ones theorem in succession.
You should try to teach others about this, but you may have
better luck
outside of school where people have not been contaminated by
false ideas.
For
example, if you are at a truck stop on the way to University
and a waiter
is
adding more than two numbers and not applying the ones therom
you should
tell
him about the ones theorem and that what he is doing is an
abomination. Be
very persistant and I guarrantee you at the end there will be
a conversion.
Bill
===
Subject: Re: addition
>> I need help with adding two numbers (like 1, 2, and maybe
even
>> others). How¹s it possible to do it without a calculator?!
Also, what
>> does it mean when the book says 1 + 1 + 1? I¹ve only heard
about
>> adding two numbers, not three. My calculus teacher wasn¹t
very clear
>> about it.
> It is considered an abomination to add a number other than
1 to another
> number. So if you are confronted with say 50 + 20 you must
break one of
these
> larger numbers down to a series of 1s to get back to basic
deŽnitions.
(Hint,
> choose the smaller one.) So we get 50 + (1 + 1 + 1 .....
+1) You move the
> Žrst 1 outside the parentheses and you get 51 + (1+1+ ....
+1) You keep
going
> like this one at a time and Žnally you will end up with 69
+ 1 = 70. The
> general result is known as the ones theorem. You must
always apply the
ones
> theroem whenever you have numbers to add together.
Is this a consequence of the axioms that natural numbers,
have just read
them, or are you just messing with the OP?
> The reason your calculus teacher would not talk about
adding three numbers
is
> that is also considered an abomination. This all goes back
to Noah¹s Ark
where
> the animals were in twos - never threes. However, you can
achieve the
same
> result by applying the ones theorem in succession.
> You should try to teach others about this, but you may have
better luck
> outside of school where people have not been contaminated
by false ideas.
For
> example, if you are at a truck stop on the way to
University and a waiter
is
> adding more than two numbers and not applying the ones
therom you should
tell
> him about the ones theorem and that what he is doing is an
abomination.
Be
> very persistant and I guarrantee you at the end there will
be a
conversion.
> Bill
--
Sigblock empty. By choice.
===
Subject: Re: addition
> Is this a consequence of the axioms that natural numbers,
have just read
> them, or are you just messing with the OP?
Not all or¹s are exclusive.
Bill
===
Subject: Re: addition
>I don¹t know who you¹re trying to impress, but there¹s no
way you can be
in
>calculus class and not know how to evaluate 1+1+1.
You¹re probably right.
On the other hand, lots of my calculus (and statistics)
students
have been unable to evaluate sums like 37/1000 + 43/1000
correctly.
The answer 80/2000 is distressingly common.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com
Address munging may or may not reduce the spam you get; it
surely
reduces the number of useful answers you get.
http://www.cs.tut.Ž/~jkorpela/usenet/laws.html
===
Subject: diagonalization
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id h9J2xcs05161;
The previous poster gave some historical remarks but did not
answer
the original poster¹s question. The diagonalization approach
will
fail for rationals because the new number created by altering
the
i¹th digit of each i¹th listed decimal will be irrational, not
rational. For proofs of the countability of the rationals,
see, for
instance, Schaum¹s
Outline of Set Theory.
--g
===
Subject: getting rid of y
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id h9J2xcK05157;
One option would be to use a trig identity: Since you have
x = sin(y) + cos(y), squaring both sides yields:
x^2 = sin^2(y)+cos^2(y)+2sin(y)cos(y). Now, since
sin^2(y)+cos^2(y)=1, you have:
x^2-1 = 2sin(y)cos(y). By a trig identity, the right hand
side can be
re-written as sin(2y); so you have:
x^2-1=sin(2y), and now you can obtain y as an explicit
function of x
by taking inverse sin of both sides.
===
Subject: Re: getting rid of y
> One option would be to use a trig identity: Since you have
> x = sin(y) + cos(y), squaring both sides yields:
> x^2 = sin^2(y)+cos^2(y)+2sin(y)cos(y). Now, since
> sin^2(y)+cos^2(y)=1, you have:
> x^2-1 = 2sin(y)cos(y). By a trig identity, the right hand
side can be
> re-written as sin(2y); so you have:
> x^2-1=sin(2y), and now you can obtain y as an explicit
function of x
> by taking inverse sin of both sides.
Slick.
===
Subject: Help on a proof for convergence?
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id h9J2xb805149;
How would one go about proving the convergence of the
following
series:
sin(n)/n
? There is no interval given. Most of the tests used for
proving
convergence cannot be used: alternating series (because the
terms are
not all decreasing, as is the case if it was only 1 to
inŽnity), the
comparison tests (you can¹t compare the series to 1/n), and
the root
and ratio tests simply make the series more difŽcult. So does
anyone
know how to prove this? Any help would be appreciated.
===
Subject: Re: Help on a proof for convergence?
> How would one go about proving the convergence of the
following
> series:
> sin(n)/n
> ? There is no interval given. Most of the tests used for
proving
> convergence cannot be used: alternating series (because the
terms are
> not all decreasing, as is the case if it was only 1 to
inŽnity), the
> comparison tests (you can¹t compare the series to 1/n), and
the root
> and ratio tests simply make the series more difŽcult. So
does anyone
> know how to prove this? Any help would be appreciated.
Hi Johnny, nice question !
I understand that you need the convergence of
S:= SUM_{k=1 to k= infty}sin(k)/k .
Try Fourier series of certain odd function f(x) such that
f(x)= SUM_{k=1 to k=infty} sin(kx)/k . Then , if possible put
x=1.
Perhaps help. Alex
Note that S_n(x):=SUM_{k=1 to k=n} sin(kx)/k >0 for all x in
(0,pi) .
This is Fejer¹s inequality (1905 ?) .
I think that you must take the 2*pi periodic odd function
f:R-->R
whose restriction at (-pi,pi] is deŽned as
f(x)= (x-pi)/pi for x in (-pi ,0)
f(x)= 0 when x=0
f(x)= (pi-x)/pi for x in (0,pi] .
If you look in a treatise on trigonometric series (A.Zygmund
or ?.Edwards)
you will see that the convergence is assured. Therefore, my
impresion
is that the sum of your series is S=f(1)=(pi-1)/pi = 1- 1/pi .
===
Subject: Re: Help on a proof for convergence?
Not helpful on any proofs, but you may Žnd this link
interesting...
http://mathworld.wolfram.com/SincFunction.html
--
Dana
= = = = = = = = = = = = = = = = =
> How would one go about proving the convergence of the
following
> series:
> sin(n)/n
> ? There is no interval given. Most of the tests used for
proving
> convergence cannot be used: alternating series (because the
terms are
> not all decreasing, as is the case if it was only 1 to
inŽnity), the
> comparison tests (you can¹t compare the series to 1/n), and
the root
> and ratio tests simply make the series more difŽcult. So
does anyone
> know how to prove this? Any help would be appreciated.
===
Subject: Re: Help on a proof for convergence?
>How would one go about proving the convergence of the
following
>series:
>sin(n)/n
>? There is no interval given. Most of the tests used for
proving
>convergence cannot be used: alternating series (because the
terms are
>not all decreasing, as is the case if it was only 1 to
inŽnity), the
>comparison tests (you can¹t compare the series to 1/n),
Can¹t you???
Obviously the denominators are equal. Can¹t you compare the
numerators?
-1 < sin(n) < 1 for any integral n. N.B. <, not <=. You know
this
because the only time sin(x) = +1 or -1 is when x = k(pi/2)+1
for
integer k. Since pi itself is irrational, k(pi/2)+1 can never
be an
integer; therefore sin(n) for integer n is never equal to +1
or -1.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com
Address munging may or may not reduce the spam you get; it
surely
reduces the number of useful answers you get.
http://www.cs.tut.Ž/~jkorpela/usenet/laws.html
===
Subject: Re: Help on a proof for convergence?
>>How would one go about proving the convergence of the
following
>>series:
Sorry, I misread that as _sequence_. Please disregard my
previous
follow-up.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com
Address munging may or may not reduce the spam you get; it
surely
reduces the number of useful answers you get.
http://www.cs.tut.Ž/~jkorpela/usenet/laws.html
===
Subject: Re: Help on a proof for convergence?
> How would one go about proving the convergence of the
following
> series:
> sin(n)/n
> ? There is no interval given.
I don¹t understand. Do you mean that the initial and Žnal
values of the
index n in the summation where not speciŽed? If so, then
perhaps you
were to assume that n goes from 1 to inŽnity. (If that¹s not
true, then
more information is needed.)
> Most of the tests used for proving convergence cannot be
used:
> alternating series (because the terms are not all
decreasing, as is the
> case if it was only 1 to inŽnity),
Right (despite the fact that MadJock seems to think that the
terms
decrease).
> the comparison tests (you can¹t compare the series to 1/n),
and the root
> and ratio tests simply make the series more difŽcult. So
does anyone
> know how to prove this? Any help would be appreciated.
If n goes from 1 to inŽnity, the series converges to (pi -
1)/2.
That series arises fairly frequently in math newsgroups. Do a
Google Groups
search for
sin(n)/n series convergence
Of course you¹ll get some stuff which isn¹t pertinent, but
you¹ll also
get what you need. The second item I found was an excellent
response by
Rob Johnson, for example.
BTW, if perchance the summation was instead supposed to be
over _all_
integers n (from -inŽnity to +inŽnity), then you would most
likely be
supposed to take sin(n)/n to be 1 when n = 0, and the sum
would then be,
neatly, just pi.
David Cantrell
===
Subject: Re: Help on a proof for convergence?
===
Subject: Help on a proof for convergence?
>How would one go about proving the convergence of the
following
>series: sin(n)/n
lim(n->oo) (sin n)/n = 0
Proof:
For eps > 0, Žnd n0 with 1/n0 < eps
Thus for all n > n0,
|(sin n)/n - 0 | = |(sin n)/n| <= 1/n < 1/n0 < eps
----
===
Subject: Re: Help on a proof for convergence?
===
> Subject: Help on a proof for convergence?
> >How would one go about proving the convergence of the
following
> >series: sin(n)/n
It¹s obvious that the _sequence_ sin(n)/n converges. But
notice the word
series above, William. Establishing convergence of the series
is not so
simple.
David
> lim(n->oo) (sin n)/n = 0
> Proof:
> For eps > 0, Žnd n0 with 1/n0 < eps
> Thus for all n > n0,
> |(sin n)/n - 0 | = |(sin n)/n| <= 1/n < 1/n0 < eps
===
Subject: Re: Help on a proof for convergence?
> >How would one go about proving the convergence of the
following
> >series: sin(n)/n
> It¹s obvious that the _sequence_ sin(n)/n converges. But
notice the word
> series above, William. Establishing convergence of the
series is not
so
> simple.
Oh, OP wants to see the series
sum_n (sin n)/n
converge. Well now that that¹s unambigious.
N modulus 2pi, is dense in the reals [0,2pi).
Thus on the average it¹s an alternating series
which makes it convergent, and also complicated.
===
Subject: Re: Help on a proof for convergence?
Weird. Seems quite obvious in my head that it converges too -
it¹s a
common
function in digital transmission systems. As n increases,
f(n) decreases.
But I don¹t know how to prove it. Sorry.
MadJock
> How would one go about proving the convergence of the
following
> series:
> sin(n)/n
> ? There is no interval given. Most of the tests used for
proving
> convergence cannot be used: alternating series (because the
terms are
> not all decreasing, as is the case if it was only 1 to
inŽnity), the
> comparison tests (you can¹t compare the series to 1/n), and
the root
> and ratio tests simply make the series more difŽcult. So
does anyone
> know how to prove this? Any help would be appreciated.
===
Subject: how would 4 9¹s equal 100 using basic math
calculations?
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id h9J62wC16584;
I would like to ask for your help in solving a mathematical
problem
that has me stumped. Lets say you have four 9¹s. Now, using
any basic
arithmetical procedure (multiply, add, divide, subtract), how
would
you get them to equal 100. Is this possible or would this be
a trick
question?
Any help would be greatly appreciated.
Eric
===
Subject: Update to problem, my actual work done
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id h9JBpEV07258;
I would like to apologize to everybody for not posting the
work I
actually did to attempt to solve this problem. Here is what I
have
done so far. Unless this is a trick question, or my math is
poor, does
this have a solution?
Addition
9 + 9 = 18 + 9 = 27 + 9 = 36
9 + 9 = 18 + 9 = 27 - 9 = 18
9 + 9 = 18 + 9 = 27 * 9 = 243
9 + 9 = 18 + 9 = 27 / 9 = 3
9 + 9 = 18 - 9 = 9 + 9 = 18
9 + 9 = 18 - 9 = 9 - 9 = 0
9 + 9 = 18 - 9 = 9 * 9 = 81
9 + 9 = 18 - 9 = 9 / 9 = 1
9 + 9 = 18 * 9 = 169 + 9 = 176
9 + 9 = 18 * 9 = 169 - 9 = 160
9 + 9 = 18 * 9 = 169 * 9 = 1521
9 + 9 = 18 * 9 = 169 / 9 = 18.77777
9 + 9 = 18 / 9 = 9 + 9 = 18
9 + 9 = 18 / 9 = 9 - 9 = 0
9 + 9 = 18 / 9 = 9 * 9 = 81
9 + 9 = 18 / 9 = 9 / 9 = 1
Subtraction
9 - 9 = 0 + 9 = 9 + 9 = 18
9 - 9 = 0 + 9 = 9 - 9 = 0
9 - 9 = 0 + 9 = 9 * 9 = 81
9 - 9 = 0 + 9 = 9 / 9 = 1
9 - 9 = 0 - 9 = -9 + 9 = 0
9 - 9 = 0 - 9 = -9 - 9 = -18
9 - 9 = 0 - 9 = -9 * 9 = -81
9 - 9 = 0 - 9 = -9 / 9 = -1
9 - 9 = 0 * 9 = 0 + 9 = 9
9 - 9 = 0 * 9 = 0 - 9 = -9
9 - 9 = 0 * 9 = 0 * 9 = 0
9 - 9 = 0 * 9 = 0 / 9 = 0
9 - 9 = 0 / 9 = 0 + 9 = 9
9 - 9 = 0 / 9 = 0 - 9 = -9
9 - 9 = 0 / 9 = 0 * 9 = 81
9 - 9 = 0 / 9 = 0 / 9 = 9
Multiplication
9 * 9 = 81 + 9 = 90 + 9 = 99
9 * 9 = 81 + 9 = 90 - 9 = 81
9 * 9 = 81 + 9 = 90 * 9 = 810
9 * 9 = 81 + 9 = 90 / 9 = 10
9 * 9 = 81 - 9 = 72 + 9 = 81
9 * 9 = 81 - 9 = 72 - 9 = 63
9 * 9 = 81 - 9 = 72 * 9 = 648
9 * 9 = 81 - 9 = 72 / 9 = 8
9 * 9 = 81 * 9 = 729 + 9 = 738
9 * 9 = 81 * 9 = 729 - 9 = 720
9 * 9 = 81 * 9 = 729 * 9 = 6561
9 * 9 = 81 * 9 = 729 / 9 = 81
9 * 9 = 81 / 9 = 9 + 9 = 18
9 * 9 = 81 / 9 = 9 - 9 = 0
9 * 9 = 81 / 9 = 9 * 9 = 81
9 * 9 = 81 / 9 = 9 / 9 = 1
Division
9 / 9 = 1 + 9 = 10 + 9 = 19
9 / 9 = 1 + 9 = 10 - 9 = 1
9 / 9 = 1 + 9 = 10 * 9 = 90
9 / 9 = 1 + 9 = 10 / 9 = 1.1111
9 / 9 = 1 - 9 = -8 + 9 = 1
9 / 9 = 1 - 9 = -8 - 9 = -17
9 / 9 = 1 - 9 = -8 * 9 = -72
9 / 9 = 1 - 9 = -8 / 9 = -0.8888
9 / 9 = 1 * 9 = 9 + 9 = 18
9 / 9 = 1 * 9 = 9 - 9 = 0
9 / 9 = 1 * 9 = 9 * 9 = 81
9 / 9 = 1 * 9 = 9 / 9 = 1
9 / 9 = 1 / 9 = 0.1111 + 9 = 9.1111
9 / 9 = 1 / 9 = 0.1111 - 9 = -8.8888
9 / 9 = 1 / 9 = 0.1111 * 9 = 1
9 / 9 = 1 / 9 = 0.1111 / 9 = 0.0123456790
Eric
===
Subject: Re: how would 4 9¹s equal 100 using basic math
calculations?
> I would like to ask for your help in solving a mathematical
problem
> that has me stumped. Lets say you have four 9¹s. Now, using
any basic
> arithmetical procedure (multiply, add, divide, subtract),
how would
> you get them to equal 100. Is this possible or would this
be a trick
> question?
99 + 9/9
===
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id h9JBpDM07210;
- when you square both sides of the original equation how do
you end
up with 2sin(y)cos(y) as I cannot see where that has come
from -
probably due to ignorance or the fact i have overlooked
something. One
other note just to be sure yogi how did the square¹s
disappear from
sin(y)y¹^2 and cos(y)y¹^2 when u took them across to the
other side -
i just need these points to check that i can go through the
process
===
>- when you square both sides of the original equation how do
you end
>up with 2sin(y)cos(y) as I cannot see where that has come
from -
Neither can I, because of the way you posted. Much as I¹d
like to
help, I can¹t.
When you¹re posting a follow-up, post it _as_ a follow-up.
Your
you¹re referring to.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com
Address munging may or may not reduce the spam you get; it
surely
reduces the number of useful answers you get.
http://www.cs.tut.Ž/~jkorpela/usenet/laws.html
===
Subject: Dont worry about the Žnding 2sinycosy bit
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id h9JBpDZ07218;
I was just being stupid - forgot for a moment that the whole
thing was
squared rather than the individual bits
===
Subject: Re: Quick Math Guide to core error issues
James,
You post so much material that I don¹t have the time or
desire to
read everything and I lose track of your position and
arguments.
Some time ago you had an organised website with deŽnitions
and cross-
reference and you have posted several summaries and histories
on this
newsgroup which would be easier to refer to if they were
permanently
available. I, for one, would be pleased if you would
resurrect your
website and put the information back.
Here are just some suggestions as to what you could put there
and
how it could be organised.
*DeŽnitions*
- Algebraic Integers and Algebraic Numbers
An explanation of what an algebraic integer is , some
examples and their general properties would be useful.
I vaguely recall that you had some software that would
take a monic quadratic equation with integer coefŽcients
and factorise it into linear terms with algebraic integer
coefŽcients. This could usefully go here as a Java applet.
- Your Object Ring¹ and what numbers are in it and what
aren¹t.
I *think* you said 2^sqrt(3) was in it
I *think* you said that it wasn¹t wholly contained in the
complex numbers
An explanation of why these numbers are in it would be useful
- What an incomplete ring is.
- Some expressions don¹t seem to translate across the
Atlantic and
I am thinking of has a factor of 5¹ in particular. To me,
has a
value of 42¹ means 42 is a value¹ so has a factor of 5¹
should
mean 5 is a factor¹ but you don¹t seem to mean this all time.
Personally, I prefer the active 5 divides N¹ or perhaps N is
divisible by 5¹ to the passive N has 5 as a factor¹.
*History*
I think you have written at least two histories to this
newsgroup
and a web site would be a much better place to put them. You
have
made several accusations of lying and you could use the
website
to substantiate them by pointing to documentation.
*Points of Contention*
Your Viewpoint
I lose track of the arguments and how they are settled or even
if they are. Your executive summary below is a good start but
that
is all it is. Hotlinks to expansions, with proofs, would be
better.
Java documentation is a fairly good example if the analogy
isn¹t
taken too far - at the top of the documentation for a class is
an explanation of what this class is for and a list of the
methods
with the types of their parameters and each has a hotlink to
an
explanation of that method. One could go further and look at
the
code but it should never be necessary.
Similarly, a mathematical exposition can have deŽnitions,
lemmas,
propositions and theorems. The proof of a lemma or similar
can cite
consequences from the statement of another but mustn¹t ever
refer to
the proof - this would be as bad as code jumping into the
middle of
a subroutine or the documentation of a method referring to the
code of another method.
I suggest an exposition of your work would have the same
structure
with an executive summary at the top and cascading expansions
of
each point. (A good book contains a series of chapters. Each
chapter
starts out by saying what it is going to say, then says it in
detail,
and Žnally ends by summarising what it has said) Your previous
website
made a point of being terse but this isn¹t necessary.
Other Viewpoints
It is not at all an easy thing to do, but if you could try to
explain,
in detail, other people¹s standpoints as well as your own
then this
would be useful. I¹m thinking in particular of the
factorisation
of certain polynomials in which you say that one root is
coprime
to a prime factor of the constant term of the polynomial and
other
people have shown explicit factorisations of the polynomial in
which this is not true. I didn¹t follow your rebuttal.
Dead Viewpoints
It would take great courage but if you could also document
points
where you are no longer holding a former position then this
also
would interesting. I¹m thinking in particular of whether a
ring
must be closed under an inŽnite summation and whether Z[pi] is
isomorphic to the reals.
*SimpliŽcations*
The polynomial that you use is very complicated with several
parameters. Is all the complication necessary to the proof
and does
it add to it? Is the u¹ term necessary at all? You have
resorted
to actually substituting values in order to explain - why not
go
back and give the whole argument again but use a polynomial
which
is as simple as possible. In fact, I don¹t always follow your
reasoning but perhaps it would be more obvious if you used a
quadratic polynomial instead of a trinomial or explained why
the
argument doesn¹t work for quadratics.
*Style*
I, too, like long sentences (my second choice for a book to
take
if I were to be stranded on a desert island would be the
collected
works of Jane Austen) and you are much better at writing them
than
I am but they can be difŽcult for other people to follow.
Take this as an example:
. I already have as the polynomial is
.
. P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2
+ u^3f)
.
. and your attempts at confusing the issue by trying to push
up x,
. don¹t help you here, as the g¹s as factors of m,
necessarily have
. a constant term with respect to m, and your claim that it
can vary
. with m, is nonsensical on its face.
It makes sense and I can understand it but I have to work at
it.
I suggest that shorter sentences would make it easier for the
reader.
Penny Hassett
> For those of you trying to keep up with the mathematical
facts in the
> discussions about the error in core mathematics from a
problem with a
> deŽnition, this post will outline the important ones
quickly and
> succinctly.
> 1. First the problematic deŽnition:
> Algebraic integers are deŽned to be roots of monic
polynomials with
> integer coefŽcient e.g. x^3 + 3x + 1 or x^234 - 34x^12 +
17, where
> monic refers to the leading coefŽcient.
> My assertion is that the over hundred year old deŽnition
excludes
> numbers that have to be included to keep from having
contradiction
> i.e. mathematical inconsistency.
> 2. The important tool I use is a polynomial:
> P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2
+ u^3 f)
> The form of the polynomial allows me to factor P(m) into
> non-polynomial factors, and the factorization with those
factors is
> P(m) = (a_1 x + uf)(a_2 x + uf)(a_3 x + uf)
> where the a¹s are roots of the following cubic:
> a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m).
> 3. Dispute centers around what happens when I divide P(m)
by f^2,
> which you¹ll note is a factor of the polynomial in the ring
of
> algebraic integers.
> 4. Mathematicians have argued that f^2 divides off as a
function of m
> because if they concede that it divides off independent of
m, then I
> can show that only two of the roots of
> a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m)
> have f as a factor.
> 5. However, it turns out that if you go to the Želd of
algebraic
> numbers you can prove that for *certain* values of m and f,
the roots
> of the cubic do not have f as a factor *in the ring of
algebraic
> numbers* which is the inconsistency.
> That is, for the math to be consistent, two of the roots
*should* have
> f as a factor as long as m and f are algebraic integers,
but while I
> can show they do for a particular values like m=1,
f=sqrt(2), there
> are other values you can show they do not *in the ring of
algebraic
> integers* which results from the deŽnition and its focus on
monic
> polynomials.
> Note: In the ring of algebraic integers you can¹t see the
problem but
> have to go to the Želd of algebraic numbers as from within
the ring
> of algebraic integers it appears that only two of the roots
have a
> factor that is f.
> James Harris
===
Subject: Re: Quick Math Guide to core error issues
> James,
> You post so much material that I don¹t have the time or
desire to
> read everything and I lose track of your position and
arguments.
> Some time ago you had an organised website with deŽnitions
and cross-
> reference and you have posted several summaries and
histories on this
> newsgroup which would be easier to refer to if they were
permanently
> available. I, for one, would be pleased if you would
resurrect your
> website and put the information back.
> Here are just some suggestions as to what you could put
there and
> how it could be organised.
> *DeŽnitions*
> - Algebraic Integers and Algebraic Numbers
> An explanation of what an algebraic integer is , some
> examples and their general properties would be useful.
> I vaguely recall that you had some software that would
> take a monic quadratic equation with integer coefŽcients
> and factorise it into linear terms with algebraic integer
> coefŽcients. This could usefully go here as a Java applet.
> - Your Object Ring¹ and what numbers are in it and what
aren¹t.
> I *think* you said 2^sqrt(3) was in it
> I *think* you said that it wasn¹t wholly contained in the
> complex numbers
> An explanation of why these numbers are in it would be
useful
> - What an incomplete ring is.
> - Some expressions don¹t seem to translate across the
Atlantic and
> I am thinking of has a factor of 5¹ in particular. To me,
has a
> value of 42¹ means 42 is a value¹ so has a factor of 5¹
should
> mean 5 is a factor¹ but you don¹t seem to mean this all
time.
> Personally, I prefer the active 5 divides N¹ or perhaps N
is
> divisible by 5¹ to the passive N has 5 as a factor¹.
> *History*
> I think you have written at least two histories to this
newsgroup
> and a web site would be a much better place to put them.
You have
> made several accusations of lying and you could use the
website
> to substantiate them by pointing to documentation.
> *Points of Contention*
> Your Viewpoint
> I lose track of the arguments and how they are settled or
even
> if they are. Your executive summary below is a good start
but that
> is all it is. Hotlinks to expansions, with proofs, would be
better.
> Java documentation is a fairly good example if the analogy
isn¹t
> taken too far - at the top of the documentation for a class
is
> an explanation of what this class is for and a list of the
methods
> with the types of their parameters and each has a hotlink
to an
> explanation of that method. One could go further and look
at the
> code but it should never be necessary.
> Similarly, a mathematical exposition can have deŽnitions,
lemmas,
> propositions and theorems. The proof of a lemma or similar
can cite
> consequences from the statement of another but mustn¹t ever
refer to
> the proof - this would be as bad as code jumping into the
middle of
> a subroutine or the documentation of a method referring to
the
> code of another method.
> I suggest an exposition of your work would have the same
structure
> with an executive summary at the top and cascading
expansions of
> each point. (A good book contains a series of chapters.
Each chapter
> starts out by saying what it is going to say, then says it
in detail,
> and Žnally ends by summarising what it has said) Your
previous
> website
> made a point of being terse but this isn¹t necessary.
> Other Viewpoints
> It is not at all an easy thing to do, but if you could try
to
> explain,
> in detail, other people¹s standpoints as well as your own
then this
> would be useful. I¹m thinking in particular of the
factorisation
> of certain polynomials in which you say that one root is
coprime
> to a prime factor of the constant term of the polynomial
and other
> people have shown explicit factorisations of the polynomial
in
> which this is not true. I didn¹t follow your rebuttal.
> Dead Viewpoints
> It would take great courage but if you could also document
points
> where you are no longer holding a former position then this
also
> would interesting. I¹m thinking in particular of whether a
ring
> must be closed under an inŽnite summation and whether Z[pi]
is
> isomorphic to the reals.
>
> *SimpliŽcations*
> The polynomial that you use is very complicated with several
> parameters. Is all the complication necessary to the proof
and does
> it add to it? Is the u¹ term necessary at all? You have
resorted
> to actually substituting values in order to explain - why
not go
> back and give the whole argument again but use a polynomial
which
> is as simple as possible. In fact, I don¹t always follow
your
> reasoning but perhaps it would be more obvious if you used a
> quadratic polynomial instead of a trinomial or explained
why the
> argument doesn¹t work for quadratics.
> *Style*
>
> I, too, like long sentences (my second choice for a book to
take
> if I were to be stranded on a desert island would be the
collected
> works of Jane Austen) and you are much better at writing
them than
> I am but they can be difŽcult for other people to follow.
> Take this as an example:
> . I already have as the polynomial is
> . P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x
u^2 + u^3f)
> . and your attempts at confusing the issue by trying to
push up x,
> . don¹t help you here, as the g¹s as factors of m,
necessarily have
> . a constant term with respect to m, and your claim that it
can vary
> . with m, is nonsensical on its face.
> It makes sense and I can understand it but I have to work
at it.
> I suggest that shorter sentences would make it easier for
the
> reader.
> Penny Hassett
>
> For those of you trying to keep up with the mathematical
facts in the
> discussions about the error in core mathematics from a
problem with a
> deŽnition, this post will outline the important ones
quickly and
> succinctly.
>
> 1. First the problematic deŽnition:
>
> Algebraic integers are deŽned to be roots of monic
polynomials with
> integer coefŽcient e.g. x^3 + 3x + 1 or x^234 - 34x^12 +
17, where
> monic refers to the leading coefŽcient.
>
> My assertion is that the over hundred year old deŽnition
excludes
> numbers that have to be included to keep from having
contradiction
> i.e. mathematical inconsistency.
>
> 2. The important tool I use is a polynomial:
>
> P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2
+ u^3 f)
>
> The form of the polynomial allows me to factor P(m) into
> non-polynomial factors, and the factorization with those
factors is
>
> P(m) = (a_1 x + uf)(a_2 x + uf)(a_3 x + uf)
>
> where the a¹s are roots of the following cubic:
>
> a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m).
>
> 3. Dispute centers around what happens when I divide P(m)
by f^2,
> which you¹ll note is a factor of the polynomial in the ring
of
> algebraic integers.
>
> 4. Mathematicians have argued that f^2 divides off as a
function of m
> because if they concede that it divides off independent of
m, then I
> can show that only two of the roots of
>
> a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m)
>
> have f as a factor.
>
> 5. However, it turns out that if you go to the Želd of
algebraic
> numbers you can prove that for *certain* values of m and f,
the roots
> of the cubic do not have f as a factor *in the ring of
algebraic
> numbers* which is the inconsistency.
>
> That is, for the math to be consistent, two of the roots
*should* have
> f as a factor as long as m and f are algebraic integers,
but while I
> can show they do for a particular values like m=1,
f=sqrt(2), there
> are other values you can show they do not *in the ring of
algebraic
> integers* which results from the deŽnition and its focus on
monic
> polynomials.
>
> Note: In the ring of algebraic integers you can¹t see the
problem but
> have to go to the Želd of algebraic numbers as from within
the ring
> of algebraic integers it appears that only two of the roots
have a
> factor that is f.
>
> James Harris
What a breath of fresh air you are on this NG!
Respectfully,
John
===
Subject: Re: Quick Math Guide to core error issues
> James,
> You post so much material that I don¹t have the time or
desire to
> read everything and I lose track of your position and
arguments.
> Some time ago you had an organised website with deŽnitions
and cross-
> reference and you have posted several summaries and
histories on this
> newsgroup which would be easier to refer to if they were
permanently
> available. I, for one, would be pleased if you would
resurrect your
> website and put the information back.
I like you Penny Hasset and appreciate your commentary which
is why
I¹m posting in a thread where I don¹t need to post as it¹s a
quide.
My problem is that I don¹t want to use MSN Groups, and I
don¹t feel
like going to another website provider.
I *am* willing to allow someone else to host my work as long
as they
give me complete editorial control.
Otherwise, it¹s easier for me to just post rather than try to
maintain
a website.
> Here are just some suggestions as to what you could put
there and
> how it could be organised.
> *DeŽnitions*
> - Algebraic Integers and Algebraic Numbers
> An explanation of what an algebraic integer is , some
> examples and their general properties would be useful.
> I vaguely recall that you had some software that would
> take a monic quadratic equation with integer coefŽcients
> and factorise it into linear terms with algebraic integer
> coefŽcients. This could usefully go here as a Java applet.
Oh yeah, after Arturo Magidin tried to make a big deal out of
some
crap, I Žgured out what he was doing, which wasn¹t much more
than a
rather simple search for a factorization in algebraic
integers.
It was fun, but not that much fun.
You see, I¹ve found and dropped more mathematics than most
people
discover in a lifetime, as I¹m a thrill seeker.
You know, an adrenaline junkie.
> - Your Object Ring¹ and what numbers are in it and what
aren¹t.
> I *think* you said 2^sqrt(3) was in it
> I *think* you said that it wasn¹t wholly contained in the
> complex numbers
> An explanation of why these numbers are in it would be
useful
Actually *you* are in it Penny Hasset, as the object ring is
rather
large.
You see, you are a mathematical object which I can prove
using some
rather basic logic and Goedel¹s proof.
I like it that you¹re in Britain.
If you¹re willing to advise me, I¹m willing to toe a line.
After all, it is math, but by myself I tend to be over the
top.
I need organization.
> - What an incomplete ring is.
It¹s a ring where you can have contradictions *within* the
ring, which
is the problem with algebraic integers.
I can explain everything, but I¹m a discoverer. I¹m an artist.
I¹m NOT organized for this other stuff, like trying to
convince
people.
I¹m an artist.
> - Some expressions don¹t seem to translate across the
Atlantic and
> I am thinking of has a factor of 5¹ in particular. To me,
has a
> value of 42¹ means 42 is a value¹ so has a factor of 5¹
should
> mean 5 is a factor¹ but you don¹t seem to mean this all
time.
> Personally, I prefer the active 5 divides N¹ or perhaps N
is
> divisible by 5¹ to the passive N has 5 as a factor¹.
Hey Penny Hasset, if you can help me, and help me overcome
these
objections to the extent that I can make some money here,
I¹ll pay you
$250,000 US from any one math prize that I win that exceeds
that
amount.
Since I¹m a black male in America, as it has a rather
stupendous
history of racism, I should be able to pay that amount as
well as
$100,000 US as previously offered to a person or group with a
machine
proof of the core error, without much trouble, since I turn
the world
upside down.
> *History*
> I think you have written at least two histories to this
newsgroup
> and a web site would be a much better place to put them.
You have
> made several accusations of lying and you could use the
website
> to substantiate them by pointing to documentation.
Oh, that¹s part of my fun. Unfortunately for me I have a
tendency to
scare people away when they Žgure out just how much I know
and what I
can do.
Luckily for me, mathematicians are arrogant *and* dumb.
So they¹re a perfect combination for someone like me, who
otherwise
gets kind of lonely.
> *Points of Contention*
> Your Viewpoint
> I lose track of the arguments and how they are settled or
even
> if they are. Your executive summary below is a good start
but that
> is all it is. Hotlinks to expansions, with proofs, would be
better.
> Java documentation is a fairly good example if the analogy
isn¹t
> taken too far - at the top of the documentation for a class
is
> an explanation of what this class is for and a list of the
methods
> with the types of their parameters and each has a hotlink
to an
> explanation of that method. One could go further and look
at the
> code but it should never be necessary.
> Similarly, a mathematical exposition can have deŽnitions,
lemmas,
> propositions and theorems. The proof of a lemma or similar
can cite
> consequences from the statement of another but mustn¹t ever
refer to
> the proof - this would be as bad as code jumping into the
middle of
> a subroutine or the documentation of a method referring to
the
> code of another method.
> I suggest an exposition of your work would have the same
structure
> with an executive summary at the top and cascading
expansions of
> each point. (A good book contains a series of chapters.
Each chapter
> starts out by saying what it is going to say, then says it
in detail,
> and Žnally ends by summarising what it has said) Your
previous
> website
> made a point of being terse but this isn¹t necessary.
I agree. Let¹s get started.
I can make you rich, if you aren¹t rich already.
If you are rich, I¹ll make you powerful.
If you¹re already powerful, hell, why not just do it?
> Other Viewpoints
> It is not at all an easy thing to do, but if you could try
to
> explain,
> in detail, other people¹s standpoints as well as your own
then this
> would be useful. I¹m thinking in particular of the
factorisation
> of certain polynomials in which you say that one root is
coprime
> to a prime factor of the constant term of the polynomial
and other
> people have shown explicit factorisations of the polynomial
in
> which this is not true. I didn¹t follow your rebuttal.
> Dead Viewpoints
> It would take great courage but if you could also document
points
> where you are no longer holding a former position then this
also
> would interesting. I¹m thinking in particular of whether a
ring
> must be closed under an inŽnite summation and whether Z[pi]
is
> isomorphic to the reals.
>
> *SimpliŽcations*
> The polynomial that you use is very complicated with several
> parameters. Is all the complication necessary to the proof
and does
> it add to it? Is the u¹ term necessary at all? You have
resorted
> to actually substituting values in order to explain - why
not go
> back and give the whole argument again but use a polynomial
which
> is as simple as possible. In fact, I don¹t always follow
your
> reasoning but perhaps it would be more obvious if you used a
> quadratic polynomial instead of a trinomial or explained
why the
> argument doesn¹t work for quadratics.
> *Style*
>
> I, too, like long sentences (my second choice for a book to
take
> if I were to be stranded on a desert island would be the
collected
> works of Jane Austen) and you are much better at writing
them than
> I am but they can be difŽcult for other people to follow.
> Take this as an example:
> . I already have as the polynomial is
> . P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x
u^2 + u^3f)
> . and your attempts at confusing the issue by trying to
push up x,
> . don¹t help you here, as the g¹s as factors of m,
necessarily have
> . a constant term with respect to m, and your claim that it
can vary
> . with m, is nonsensical on its face.
> It makes sense and I can understand it but I have to work
at it.
> I suggest that shorter sentences would make it easier for
the
> reader.
> Penny Hassett
I like it Penny Hassett, and I¹m willing to do some work, but
not much
as I¹m the engine that drive everything anyway.
You prepare to do some work--and make no mistake you WILL
work very
hard--and I¹ll try to give you success.
After all, I¹m already one of the most powerful men on the
planet.
With your help, I can get organized and maybe do some good in
this
world.
Email me if you¹re interested, all offers are rescinded if
you do not.
James Harris
===
Subject: Re: Quick Math Guide to core error issues
>>James,
>>You post so much material that I don¹t have the time or
desire to
>>read everything and I lose track of your position and
arguments.
>>Some time ago you had an organised website with deŽnitions
and cross-
>>reference and you have posted several summaries and
histories on this
>>newsgroup which would be easier to refer to if they were
permanently
>>available. I, for one, would be pleased if you would
resurrect your
>>website and put the information back.
> I like you Penny Hasset and appreciate your commentary
which is why
> I¹m posting in a thread where I don¹t need to post as it¹s
a quide.
> My problem is that I don¹t want to use MSN Groups, and I
don¹t feel
> like going to another website provider.
> I *am* willing to allow someone else to host my work as
long as they
> give me complete editorial control.
> Otherwise, it¹s easier for me to just post rather than try
to maintain
> a website.
http:www.sphosting.com is easy to use, and allows Žle
uploading. Of
course, if you aren¹t willing to do any work, by all means
keep everyone
somewhat confused and off-balance.
Perhaps you could post a weekly update?
--
Will Twentyman
email: wtwentyman at copper dot net
===
Subject: Re: Quick Math Guide to core error issues
> as I¹m the engine that drive everything anyway.
> You prepare to do some work--and make no mistake you WILL
work very
> hard--and I¹ll try to give you success.
> After all, I¹m already one of the most powerful men on the
planet.
> With your help, I can get organized and maybe do some good
in this
> world.
> Email me if you¹re interested, all offers are rescinded if
you do not.
> James Harris
of you material up on a web-site then I¹m willing to advise
on the
format and style by way of the sci.math newsgroup but that¹s
all.
PS. Lest you feel I am being dishonest when you Žnd out
later, let
me say that it will be obvious to many people in Britain that
I am using a nom-de-keyboard.
===
Subject: Re: Quick Math Guide to core error issues
> I like it Penny Hassett, and I¹m willing to do some work,
but not much
> as I¹m the engine that drive everything anyway.
>
> You prepare to do some work--and make no mistake you WILL
work very
> hard--and I¹ll try to give you success.
>
> After all, I¹m already one of the most powerful men on the
planet.
>
> With your help, I can get organized and maybe do some good
in this
> world.
>
> Email me if you¹re interested, all offers are rescinded if
you do not.
>
> James Harris
> of you material up on a web-site then I¹m willing to advise
on the
> format and style by way of the sci.math newsgroup but
that¹s all.
last couple of days, partly out of EXTREME FRUSTRATION at my
situation. I¹ve found that I can have fun with postings,
which makes
me feel better.
Still I was sincere about the $250k but am now relieved that
you
declined.
Oh yeah, I¹ve taken your advice though as I¹m using only m as
a
variable in my recent postings as I¹m *really* ready to Žnish
things
up.
> PS. Lest you feel I am being dishonest when you Žnd out
later, let
> me say that it will be obvious to many people in Britain
that
> I am using a nom-de-keyboard.
Oh hey, I¹d started calling you my money penny too. Kind of
like a
James thing, you know, Bond, James Bond.
Oh well, maybe someday you¹ll have reason to give me your
name, but
it¹s not a big deal. In any event, unlike with Nora Baron, I
won¹t
put quotes around your name.
James Harris
===
Subject: Re: Quick Math Guide to core error issues
> I¹m willing to do some work, but not much
I knew it! You¹re just too lazy!
===
Subject: Re: Quick Math Guide to core error issues
putting aside the question of wether there is *any* real JSH,
I still have to question this one¹s entitlement to the name,
when he goes over the top and says that a correspondent can
be proved to be in his newfound ring of what ever.
back to teh question of the real one:
if he¹s not being paid to do this, or has a pension
that is allowing him to make fun of Whitey (?),
then it really is pretty strange.
note on Anglo-american history:
slavery was a British institution;
that¹s why they supported the Confederacy (along
with the New York Times etc.) with ships & materiel,
and actually organized the Civil War. (this makes
for a good, revisionist question:
What was our 3rd war with Great Britain?)
[see http://tarpley.net]
> I¹m posting in a thread where I don¹t need to post as it¹s
a quide.
> An explanation of what an algebraic integer is , some
> examples and their general properties would be useful.
> I vaguely recall that you had some software that would
> take a monic quadratic equation with integer coefŽcients
> and factorise it into linear terms with algebraic integer
> coefŽcients. This could usefully go here as a Java applet.
> You see, I¹ve found and dropped more mathematics than most
people
> Actually *you* are in it Penny Hasset, as the object ring
is rather
> large.
> You see, you are a mathematical object which I can prove
using some
> rather basic logic and Goedel¹s proof.
> I like it that you¹re in Britain.
> I lose track of the arguments and how they are settled or
even
> if they are. Your executive summary below is a good start
but that
> is all it is. Hotlinks to expansions, with proofs, would be
better.
> If you¹re already powerful, hell, why not just do it?
> It would take great courage but if you could also document
points
> where you are no longer holding a former position then this
also
> would interesting. I¹m thinking in particular of whether a
ring
> must be closed under an inŽnite summation and whether Z[pi]
is
> isomorphic to the reals.
> . I already have as the polynomial is
> .
> . P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x
u^2 +
u^3f)
> .
> . and your attempts at confusing the issue by trying to
push up x,
> . don¹t help you here, as the g¹s as factors of m,
necessarily have
> . a constant term with respect to m, and your claim that it
can vary
> . with m, is nonsensical on its face.
--UN HYDROGEN (sic; Methanex (TM) reformanteurs) ECONOMIE?...
La Troi Phases d¹Exploitation de la Protocols des Grises de
Kyoto:
(FOSSILISATION [McCainanites?] (TM/sic))/
BORE/GUSH/NADIR @ http://www.tarpley.net/aobook.htm.
Http://www.tarpley.net/bushb.htm (content partiale, below):
17 -- L¹ATTEMPTER de COUP D¹ETAT, 3/30/81
===
Subject: Re: Quick Math Guide to core error issues
> [...]
> note on Anglo-american history:
> slavery was a British institution;
The British slave traders bought their slaves from Arab and
African
trade slavers, so it wasn¹t a British institution it was an
international one. Slavery persists to this day of course.
> [...]
--
G.C.
===
Subject: Re: Quick Math Guide to core error issues
> For those of you trying to keep up with the mathematical
facts in the
> discussions about the error in core mathematics from a
problem with a
> deŽnition, this post will outline the important ones
quickly and
> succinctly.
> 1. First the problematic deŽnition:
> Algebraic integers are deŽned to be roots of monic
polynomials with
> integer coefŽcient e.g. x^3 + 3x + 1 or x^234 - 34x^12 +
17, where
> monic refers to the leading coefŽcient.
> My assertion is that the over hundred year old deŽnition
excludes
> numbers that have to be included to keep from having
contradiction
> i.e. mathematical inconsistency.
This is sheer idiocy.
A deŽnition cannot lead to a contradiction.
A deŽnition, that is not correctly understood by a wannabe
maths genius
like yourself, followed by some ridiculously confused
attempts at
proving things, can lead a sufŽciently stupid person to
thinking there
are contradictions. But that is _your_ problem, and not a
problem of the
deŽnition.
===
Subject: Re: Quick Math Guide to core error issues
In sci.physics, James Harris
discussions about the error in core mathematics from a
problem with a
> deŽnition, this post will outline the important ones
quickly and
> succinctly.
> 1. First the problematic deŽnition:
> Algebraic integers are deŽned to be roots of monic
polynomials with
> integer coefŽcient e.g. x^3 + 3x + 1 or x^234 - 34x^12 +
17, where
> monic refers to the leading coefŽcient.
> My assertion is that the over hundred year old deŽnition
excludes
> numbers that have to be included to keep from having
contradiction
> i.e. mathematical inconsistency.
And these numbers are ... what? Presumably, you can produce
a counterexample.
> 2. The important tool I use is a polynomial:
> P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2
+ u^3 f)
> The form of the polynomial allows me to factor P(m) into
> non-polynomial factors, and the factorization with those
factors is
> P(m) = (a_1 x + uf)(a_2 x + uf)(a_3 x + uf)
> where the a¹s are roots of the following cubic:
> a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m).
Pedant point: ITYM a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2
f^2 + 3m) = 0.
> 3. Dispute centers around what happens when I divide P(m)
by f^2,
> which you¹ll note is a factor of the polynomial in the ring
of
> algebraic integers.
That it is, for what it¹s worth. However, you¹ve not gotten
around the f^(2/3) problem yet. I posit that a perfectly
valid transformation of your cubic is
Q(m) = P(m) / f^2 = (b_1 x + uf^(1/3))(b_2 x + uf^(1/3))(b_3
x + uf^(1/3))
where b_{i} = a_{i} / f^(2/3).
In fact, that¹s probably what you¹d end up with anyway! :-)
I, however, make no claims regarding the b_{i} being
integers, algebraic or otherwise. I¹m not sure what
can be deduced therefrom.
It¹s worth noting that f^(1/3) is an algebraic integer if f
is.
Another transformation is
R(m) = P(m) / f^3 = (c_1 x + u)(c_2 x + u) (c_3 x + u)
although in this case we have a problem, as not all the c¹s
are algebraic integers; there¹s a missing factor of 1/f in
there somewhere. This factor can be added in:
Q(m) = f R(m) = (c_1 x + u) (c_2 x + u) (c_3 fx + uf)
but it could equally easily be added in:
Q(m) = (c_1 f^(1/3) x + u f^(1/3)) (c_2 f^(1/3) x + u f^(1/3))
(c_3 f^(1/3)x + uf^(1/3))
or
Q(m) = (c_1 x + u) ( c_2 f^(1/2) x + u f^(1/2) ) (c_3 f^(1/2)
x + u
f^(1/2))
I just don¹t know at this point.
> 4. Mathematicians have argued that f^2 divides off as a
function of m
> because if they concede that it divides off independent of
m, then I
> can show that only two of the roots of
> a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m)
> have f as a factor.
If one sets f = 2, m = 1 we get
a^3 + 9a^2 - 28
which has as one root a_1 = -2. Factoring, we get
a^3 + 9a^2 - 28 = (a + 2) (a^2 + 7a - 14)
so the other two roots are a_x = (-7 ± sqrt(49 + 56)) / 2
= -7/2 ± sqrt(105) / 2.
Only one of these roots (-2) is divisible by 2. The other
two roots
-7/2 ± sqrt(105) / 2
are such that, if we set b_x = a_x/2, or a_x = 2b_x, we get
b_x = -7/4 ± sqrt(105) / 4.
What equation of integer coefŽcients does the b¹s satisfy?
That¹s simple enough; substituting 2b for a, we get
4b^2 + 14b - 14 = 0
or
2b^2 + 7b - 7 = 0.
Clearly, the b¹s are not algebraic integers, and therefore
two of the original a¹s are not divisible by 2, for this
particular setting of f and m.
This is a counterexample to your original proposition.
> 5. However, it turns out that if you go to the Želd of
algebraic
> numbers you can prove that for *certain* values of m and f,
the roots
> of the cubic do not have f as a factor *in the ring of
algebraic
> numbers* which is the inconsistency.
> That is, for the math to be consistent, two of the roots
*should* have
> f as a factor as long as m and f are algebraic integers,
but while I
> can show they do for a particular values like m=1,
f=sqrt(2), there
> are other values you can show they do not *in the ring of
algebraic
> integers* which results from the deŽnition and its focus on
monic
> polynomials.
I take it you want to include
-7/4 ± sqrt(105) / 4
in the ring of algebraic integers?
Please clarify.
> Note: In the ring of algebraic integers you can¹t see the
problem but
> have to go to the Želd of algebraic numbers as from within
the ring
> of algebraic integers it appears that only two of the roots
have a
> factor that is f.
2/3 can be divided by 3 (the result being 2/9). Did you have a
point here?
> James Harris
--
#191, ewill3@earthlink.net
It¹s still legal to go .sigless.
===
Subject: Re: Quick Math Guide to core error issues
> In sci.physics, James Harris
>
...
> 5. However, it turns out that if you go to the Želd of
algebraic
> numbers you can prove that for *certain* values of m and f,
the roots
> of the cubic do not have f as a factor *in the ring of
algebraic
> numbers* which is the inconsistency.
>
> That is, for the math to be consistent, two of the roots
*should* have
> f as a factor as long as m and f are algebraic integers,
but while I
> can show they do for a particular values like m=1,
f=sqrt(2), there
> are other values you can show they do not *in the ring of
algebraic
> integers* which results from the deŽnition and its focus on
monic
> polynomials.
> I take it you want to include
> -7/4 ± sqrt(105) / 4
> in the ring of algebraic integers?
No, he can not add both. Their sum is -7/2, and adding both
would make
2 a unit. He wants to add only one, but he will not tell us
which one.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam,
nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
===
Subject: Re: Quick Math Guide to core error issues
In sci.physics, Dik T. Winter
:
> In sci.physics, James Harris
> 5. However, it turns out that if you go to the Želd of
algebraic
> numbers you can prove that for *certain* values of m and f,
the roots
> of the cubic do not have f as a factor *in the ring of
algebraic
> numbers* which is the inconsistency.
>
> That is, for the math to be consistent, two of the roots
*should*
have
> f as a factor as long as m and f are algebraic integers,
but while I
> can show they do for a particular values like m=1,
f=sqrt(2), there
> are other values you can show they do not *in the ring of
algebraic
> integers* which results from the deŽnition and its focus on
monic
> polynomials.
>
> I take it you want to include
> -7/4 ± sqrt(105) / 4
> in the ring of algebraic integers?
> No, he can not add both. Their sum is -7/2, and adding both
would make
> 2 a unit. He wants to add only one, but he will not tell us
which one.
It¹s a package deal. :-) And he gets 4 for the price of 2; the
reciprocals need to be added as well, as unit * unit = unit
and unit / unit = unit.
In fact, a lot more will be dragged in by this inclusion. But
the original deŽnition discriminates against this number
(and for good reason).
--
#191, ewill3@earthlink.net
It¹s still legal to go .sigless.
===
Subject: Re: Quick Math Guide to core error issues
> For those of you trying to keep up with the mathematical
facts in the
> discussions about the error in core mathematics from a
problem with a
> deŽnition, this post will outline the important ones
quickly and
> succinctly.
> 1. First the problematic deŽnition:
> Algebraic integers are deŽned to be roots of monic
polynomials with
> integer coefŽcient e.g. x^3 + 3x + 1 or x^234 - 34x^12 +
17, where
> monic refers to the leading coefŽcient.
> My assertion is that the over hundred year old deŽnition
excludes
> numbers that have to be included to keep from having
contradiction
> i.e. mathematical inconsistency.
The deŽnition just deŽnes a set of numbers. The deŽnition
itself cannot produce a contradiction. Contradictions are
produced when one theorem¹ contradicts another theorem.
If you think you have a contradiction here, what is the
known theorem in algebraic number theory which is being
contradicted? (See below at {###] for my speculation on this.)
> 2. The important tool I use is a polynomial:
> P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2
+ u^3 f)
> The form of the polynomial allows me to factor P(m) into
> non-polynomial factors, and the factorization with those
factors is
> P(m) = (a_1 x + uf)(a_2 x + uf)(a_3 x + uf)
> where the a¹s are roots of the following cubic:
> a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m).
... and the a¹s are therefore algebraic integers (this cubic
is monic).
> 3. Dispute centers around what happens when I divide P(m)
by f^2,
> which you¹ll note is a factor of the polynomial in the ring
of
> algebraic integers.
> 4. Mathematicians have argued that f^2 divides off as a
function of m
> because if they concede that it divides off independent of
m, then I
> can show that only two of the roots of
>[*] a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m)
> have f as a factor.
No - we don¹t argue that it divides off as a function of
m. We argue essentially that f^2 is distributed among the
factors (ai*x + u*f) in a way which depends on m. For example,
if m is such that the polynomial [*] that you give above is
reducible, then one factor is relatively prime to f. But if
m is such that [*] is irreducible, then *none* of the factors
are relatively prime to f. In fact in the irreducible case,
ALL of the factors (ai*x + u*f) are divisible by f^{2/3}.
See my post of Oct 18 in the thread Finishing argument - core
error proven for a proof of this.
> 5. However, it turns out that if you go to the Želd of
algebraic
> numbers you can prove that for *certain* values of m and f,
the roots
> of the cubic do not have f as a factor *in the ring of
algebraic
> numbers* which is the inconsistency.
The Žrst part is true: it happens whenever [*] is irreducible,
which is true for most values of m. But it does not result
in a contradiction. The factorization is different when the
polynomial [*] is irreducible than when it is not. The twain
do not meet (i.e., [*] is either irreducible or it is not)
so there is no inconsistency.
> That is, for the math to be consistent, two of the roots
*should* have
> f as a factor as long as m and f are algebraic integers,
but while I
> can show they do for a particular values like m=1,
f=sqrt(2), there
> are other values you can show they do not *in the ring of
algebraic
> integers* which results from the deŽnition and its focus on
monic
> polynomials.
f = sqrt(2) is of no interest here. You original concern,
relevant
not only to your claims in Advanced Polynomial Factorization
and Core
error but also to your proof of Fermat¹s last theorem, dealt
with f a
a prime > 3 and m an integer relatively prime to f. Our
counterexamples
to your argument are restricted to the latter conditions. But
even if one
wanted to generalize for formal academic reasons: how f^2
distributes among
the factors (a1*x + u*f) differs as described above for
different
combinations of m and f. Proving something about the form of
the
factorization for one combination does not prove it for
others, as
you inexplicably seem to believe.
Similarly proving that for m = 0, f^2 distributes into the 3
factors as f, f, and 1, tells you nothing about cases for
which
m <> 0. I am surprised to see that you have mentioned your
erroneous
belief to the contrary, for the thousandth time.
> Note: In the ring of algebraic integers you can¹t see the
problem but
> have to go to the Želd of algebraic numbers as from within
the ring
> of algebraic integers it appears that only two of the roots
have a
> factor that is f.
A bizarre statement. In the Želd of algebraic numbers, every
number has f as a factor! This is of no interest at all. The
whole point of what you have been doing is lost if you decide
to
start talking about factorizations in a Želd.
Nora B.
> James Harris
[###]
Your result, if true, would contradict one of the
following theorems:
1. Roots of non-monic primitive irreducible polynomial with
integer coefŽcients cannot be algebraic integers.
2. The set of algebraic numbers constitutes a ring.
I think you are refusing to say that your result contradicts
1. because you have gone on record (in 2002) as accepting that
1. is a correct theorem. You have not thought much about 2.,
which is also a theorem and one which is moderately difŽcult
to
prove. You have chosen to say that your result follows from
an error in the deŽnition of algebraic integers because you
know that would lead to the conclusion that mathematics is
inconsistent (which you and the rest of us abhor), OR that
your own proof is wrong. And your emotional state is such
that you cannot possibly accept the latter conclusion. But
saying that your result is a consequence of an erroneous
deŽnition makes no sense at all on any scale.
N.B.
===
Subject: Re: Quick Math Guide to core error issues
Adjunct Assistant Professor at the University of Montana.
[.snip.]
>> 4. Mathematicians have argued that f^2 divides off as a
function of m
>> because if they concede that it divides off independent of
m, then I
>> can show that only two of the roots of
>>[*] a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m)
>> have f as a factor.
> No - we don¹t argue that it divides off as a function of
>m. We argue essentially that f^2 is distributed among the
>factors (ai*x + u*f) in a way which depends on m. For
example,
>if m is such that the polynomial [*] that you give above is
>reducible, then one factor is relatively prime to f.
This is not true in general either. If m=1 and f=2, one
factor is a
multiple of f, and the other two are multiples of proper
factors of f;
the polynomial [*] in that case factors as a product of a
linear and
an irreducible quadratic.
What we have said is that:
> But if
>m is such that [*] is irreducible, then *none* of the factors
>are relatively prime to f.
But there have been no general conclusions about the
reducible case in
general, other than it may indeed be the case that one of the
factors
is coprime to f.
Why do you take so much trouble to expose such a reasoner as
Mr. Smith? I answer as a deceased friend of mine used to
answer
on like occasions - A man¹s capacity is no measure of his
power
to do mischief. Mr. Smith has untiring energy, which does
something; self-evident honesty of conviction, which does
more;
and a long purse, which does most of all. He has made at least
ten publications, full of Žgures few readers can criticize. A
great
many people are staggered to this extent, that they imagine
there
must be the indeŽnite something in the mysterious all this.
They are brought to the point of suspicion that the
mathematicians
ought not to treat all this with such undisguised contempt,
at least.
-- A Budget of Paradoxes, Vol. 2 p. 129 by Augustus de Morgan
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: Quick Math Guide to core error issues
...
> 1. First the problematic deŽnition:
>
> Algebraic integers are deŽned to be roots of monic
polynomials with
> integer coefŽcient e.g. x^3 + 3x + 1 or x^234 - 34x^12 +
17, where
> monic refers to the leading coefŽcient.
>
> My assertion is that the over hundred year old deŽnition
excludes
> numbers that have to be included to keep from having
contradiction
> i.e. mathematical inconsistency.
> The deŽnition just deŽnes a set of numbers. The deŽnition
> itself cannot produce a contradiction. Contradictions are
> produced when one theorem¹ contradicts another theorem.
> If you think you have a contradiction here, what is the
> known theorem in algebraic number theory which is being
> contradicted? (See below at {###] for my speculation on
this.)
...
> Your result, if true, would contradict one of the
> following theorems:
> 1. Roots of non-monic primitive irreducible polynomial with
> integer coefŽcients cannot be algebraic integers.
> 2. The set of algebraic numbers constitutes a ring.
You mean algebraic integers here.
> I think you are refusing to say that your result contradicts
> 1. because you have gone on record (in 2002) as accepting
that
> 1. is a correct theorem. You have not thought much about 2.,
> which is also a theorem and one which is moderately
difŽcult to
> prove.
Actually he is also on record accepting that 2 is true, the
last time
was not so long ago.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam,
nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
===
Subject: Re: Quick Math Guide to core error issues
> For those of you trying to keep up with the mathematical
facts in the
> discussions about the error in core mathematics from a
problem with a
> deŽnition, this post will outline the important ones
quickly and
> succinctly.
> 1. First the problematic deŽnition:
> Algebraic integers are deŽned to be roots of monic
polynomials with
> integer coefŽcient e.g. x^3 + 3x + 1 or x^234 - 34x^12 +
17, where
> monic refers to the leading coefŽcient.
> My assertion is that the over hundred year old deŽnition
excludes
> numbers that have to be included to keep from having
contradiction
> i.e. mathematical inconsistency.
> The deŽnition just deŽnes a set of numbers. The deŽnition
> itself cannot produce a contradiction. Contradictions are
> produced when one theorem¹ contradicts another theorem.
> If you think you have a contradiction here, what is the
> known theorem in algebraic number theory which is being
> contradicted? (See below at {###] for my speculation on
this.)
> 2. The important tool I use is a polynomial:
> P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2
+ u^3 f)
> The form of the polynomial allows me to factor P(m) into
> non-polynomial factors, and the factorization with those
factors is
> P(m) = (a_1 x + uf)(a_2 x + uf)(a_3 x + uf)
> where the a¹s are roots of the following cubic:
> a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m).
> ... and the a¹s are therefore algebraic integers (this cubic
> is monic).
> 3. Dispute centers around what happens when I divide P(m)
by f^2,
> which you¹ll note is a factor of the polynomial in the ring
of
> algebraic integers.
> 4. Mathematicians have argued that f^2 divides off as a
function of m
> because if they concede that it divides off independent of
m, then I
> can show that only two of the roots of
>[*] a^3 + 3(-1+mf^2)a^2 - f^2(m^3 f^4 - 3m^2 f^2 + 3m)
> have f as a factor.
> No - we don¹t argue that it divides off as a function of
> m. We argue essentially that f^2 is distributed among the
> factors (ai*x + u*f) in a way which depends on m. For
example,
> if m is such that the polynomial [*] that you give above is
> reducible, then one factor is relatively prime to f. But if
> m is such that [*] is irreducible, then *none* of the
factors
> are relatively prime to f. In fact in the irreducible case,
> ALL of the factors (ai*x + u*f) are divisible by f^{2/3}.
> See my post of Oct 18 in the thread Finishing argument -
core
> error proven for a proof of this.
> 5. However, it turns out that if you go to the Želd of
algebraic
> numbers you can prove that for *certain* values of m and f,
the roots
> of the cubic do not have f as a factor *in the ring of
algebraic
> numbers* which is the inconsistency.
> The Žrst part is true: it happens whenever [*] is
irreducible,
> which is true for most values of m. But it does not result
> in a contradiction. The factorization is different when the
> polynomial [*] is irreducible than when it is not. The twain
> do not meet (i.e., [*] is either irreducible or it is not)
> so there is no inconsistency.
> That is, for the math to be consistent, two of the roots
*should* have
> f as a factor as long as m and f are algebraic integers,
but while I
> can show they do for a particular values like m=1,
f=sqrt(2), there
> are other values you can show they do not *in the ring of
algebraic
> integers* which results from the deŽnition and its focus on
monic
> polynomials.
> f = sqrt(2) is of no interest here. You original concern,
relevant
> not only to your claims in Advanced Polynomial
Factorization and
Core
> error but also to your proof of Fermat¹s last theorem,
dealt with f
a
> a prime > 3 and m an integer relatively prime to f. Our
counterexamples
> to your argument are restricted to the latter conditions.
But even if
one
> wanted to generalize for formal academic reasons: how f^2
distributes
among
> the factors (a1*x + u*f) differs as described above for
different
> combinations of m and f. Proving something about the form
of the
> factorization for one combination does not prove it for
others, as
> you inexplicably seem to believe.
> Similarly proving that for m = 0, f^2 distributes into the 3
> factors as f, f, and 1, tells you nothing about cases for
which
> m <> 0. I am surprised to see that you have mentioned your
erroneous
> belief to the contrary, for the thousandth time.
> Note: In the ring of algebraic integers you can¹t see the
problem but
> have to go to the Želd of algebraic numbers as from within
the ring
> of algebraic integers it appears that only two of the roots
have a
> factor that is f.
> A bizarre statement. In the Želd of algebraic numbers, every
> number has f as a factor! This is of no interest at all. The
> whole point of what you have been doing is lost if you
decide to
> start talking about factorizations in a Želd.
> Nora B.
> James Harris
> [###]
> Your result, if true, would contradict one of the
> following theorems:
> 1. Roots of non-monic primitive irreducible polynomial with
> integer coefŽcients cannot be algebraic integers.
> 2. The set of algebraic numbers constitutes a ring.
> I think you are refusing to say that your result contradicts
> 1. because you have gone on record (in 2002) as accepting
that
> 1. is a correct theorem. You have not thought much about 2.,
> which is also a theorem and one which is moderately
difŽcult to
> prove. You have chosen to say that your result follows from
> an error in the deŽnition of algebraic integers because you
> know that would lead to the conclusion that mathematics is
> inconsiste